A215189 Array t(n,k) of the family ((n+k)/gcd(n+k,4))*(n/gcd(n,4)), read by antidiagonals.

0, 1, 0, 1, 1, 0, 9, 3, 3, 0, 1, 3, 1, 1, 0, 25, 5, 15, 5, 5, 0, 9, 15, 3, 9, 3, 3, 0, 49, 21, 35, 7, 21, 7, 7, 0, 4, 14, 6, 10, 2, 6, 2, 2, 0, 81, 18, 63, 27, 45, 9, 27, 9, 9, 0, 25, 45, 10, 35, 15, 25, 5, 15, 5, 5, 0, 121, 55, 99, 22, 77, 33, 55, 11, 33, 11, 11, 0, 9, 33, 15, 27, 6, 21, 9, 15, 3, 9, 3, 3, 0

Offset: 0

Author

Jean-François Alcover, Jun 12 2013

Keywords

• nonn
• tabl

Comments

Identification of rows and columns:

Row 2, n=1: A060819,

row 3, n=2: A060819 (shifted),

row 4, n=3: A068219,

row 5, n=4: A060819 (shifted),

row 6, n=5: A060819 (shifted and multiplied by 5),

row 7, n=6: A068219 (shifted),

row 8, n=7: A060819 (shifted and multiplied by 7);

column 1, k=0: A181318,

column 2, k=1: A064038,

column 3, k=2: A198148,

column 4, k=3: A160050,

column 5, k=4: A061037,

column 6, k=5: A178242,

column 7, k=6: A217366,

column 8, k=7: A217367.

This array is the transposition of the array given by Paul Curtz in the comments in A181318.

Examples

			Array begins:
   0,  0,  0,  0,  0,  0,  0, ...
   1,  1,  3,  1,  5,  3,  7, ...
   1,  3,  1,  5,  3,  7,  2, ...
   9,  3, 15,  9, 21,  6, 27, ...
   1,  5,  3,  7,  2,  9,  5, ...
  25, 15, 35, 10, 45, 25, 55, ...
   9, 21,  6, 27, 15, 33,  9, ...
  49, 14, 63, 35, 77, 21, 91, ...
  ...
Triangle begins:
    0;
    1,  0;
    1,  1,  0;
    9,  3,  3,  0;
    1,  3,  1,  1,  0;
   25,  5, 15,  5,  5,  0;
    9, 15,  3,  9,  3,  3,  0;
   49, 21, 35,  7, 21,  7,  7,  0;
    4, 14,  6, 10,  2,  6,  2,  2,  0;
   81, 18, 63, 27, 45,  9, 27,  9,  9,  0;
   25, 45, 10, 35, 15, 25,  5, 15,  5,  5,  0;
  121, 55, 99, 22, 77, 33, 55, 11, 33, 11, 11,  0;
    9, 33, 15, 27,  6, 21,  9, 15,  3,  9,  3,  3,  0;
  ...
		

Links

• G. C. Greubel, Antidiagonals n=0..100 of triangle, flattened

Crossrefs

Cf. A060819, A181318, A064038, A198148, A160050, A061037, A178242, A217366, A217367.

Programs

Magma

/* As triangle: */ [[(n-k)/GCD(n-k, 4)*n/GCD(n, 4): k in [0..n]]: n in [0..12]]; // Bruno Berselli, Jun 13 2013

Mathematica

t[n_, k_] := (n+k)/GCD[n+k, 4]*n/GCD[n, 4];  Table[t[n-k, k], {n, 0, 12}, {k, 0, n}] // Flatten

Formula

t(n,k) = ((n+k)/gcd(n+k,4))*(n/gcd(n,4)).